When Amir says, "I don't want to forget anymore," he is saying that he is ready to face what happened to Hassan the day Amir won the kite championship and Hassan ran it for him. Hassan was raped and Amir stood by and watched in the shadows not helping his only true friend in the world. Amir never mentions the incident and he tried so hard to bury it. He even went so far as to accuse Hassan of stealing his birthday gifts so that his father would send Hassan and his father away. He didn't want to have to look at him or be friends with him any longer because Amir could barely stand his own reflection when he was faced with what happened to Hassan.

After living with the guilt and shame of what he had done to Hassan he was finally ready, as an adult, to face it and try to redeem himself in some way. Rahim Kahn, Baba's trusted friend, calls upon Amir and tells him, "there is a way to be good again." Amir cannot resist the offer at a chance to make things right and it is then that he admits to himself that he does not want to forget anymore.